Where do start my search for nursing care?

Try to book the bulkhead seats in the airplane . More room to get her in and out . Tell the airline she will need the aisle wheelchair.

I find it very easy to travel with my husband with Parkinson, no dementia, no incontinence and he is fairly mobile mostly with walker, but as per IATA rules airlines have to provide assistance to people with disabilities. We go thru crew security never wait in lines, in many ways we avoid all the hassle.
We usually book at least bus class, close to washroom.
Some airlines have wheelchair on board, not all.
I find assistance if needed locally.
Last year my husband had 2 surgeries out of country one was fairly major and drs declared him OK to travel after week or 10 days.

I'm not sure any airplane aisle is wide enough for a standard wheelchair so you'd have to confirm this with the airlines. I think your LO will first have to be transferred into a special "aisle chair" and then into their seat. Also, depending on the surgery, the airlline may not permit your LO to travel so be sure to ask this question before you buy a ticket.

Also, you need to ask the doctor if your LO should fly soon after surgery because it can increase the risk of blood clots, which can be fatal.

This website states that a recent surgery may be grounds for the airlines to deny service.

https://www.medical-air-service.com/blog/medical-conditions-that-prevent-you-from-flying-commercially-why-are-you-not-allowed-on-board_8169.html

It will be difficult for your LO to use the bathroom during the flight, so keep this in mind as well.

You need to contact a home care agency and ask for a CNA who is willing to travel.